Thermodynamics in very strong coupling: A possible model for the high-Tcoxides

We have calculated the thermodynamic properties of an isotropic electron-phonon superconductor in the very-strong-coupling regime which results when the critical temperature ($T_c$) is on the order of a typical phonon energy. In this limit $\frac{2{\Delta }_0}{k_B{T}_c}$, with ${\Delta }_0$ the gap edge, is much larger than the Bardeen-Cooper-Schrieffer (BCS) value of 3.54 while at the same time the other dimensionless thermodynamic indices would indicate weak coupling. In fact $\frac{\Delta C\left(T_c\right)}{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c}$, with $\Delta C\left(T_c\right)$ the specific-heat jump and $\gamma \mathrm{}\left(0\right)\mathrm{}$ the Sommerfeld constant, can be less than 1.43 and the ratio $\frac{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c^2}{H_c^2\mathrm{}\left(0\right)\mathrm{}}$, with $H_c\mathrm{}\left(0\right)\mathrm{}$ the zero-temperature thermodynamic critical magnetic field, greater than 0.168. Also the critical-field deviation function is negative definite and smaller than in BCS. All these results are in striking contrast to the usual modest strong-coupling corrections that apply in conventional superconductors and, except for $\frac{2{\Delta }_0}{k_B{T}_c}$, are in the opposite direction.